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Proper quantization rule approach to three‐dimensional quantum dots
Author(s) -
Serrano Fernando Adan,
Dong ShiHai
Publication year - 2013
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.24449
Subject(s) - quantization (signal processing) , formalism (music) , harmonic oscillator , physics , quantum mechanics , quantum dot , radius , coulomb , classical mechanics , brillouin zone , quantum , electron , mathematics , art , musical , computer security , algorithm , computer science , visual arts
In this article, we develop a formalism to obtain the energy levels of the electron in a central force potential confined in a spherical quantum dot with radius r C by the proper quantization rule and the Wentzel‐Kramers‐Brillouin approximation. It is shown that the numerical results are in good agreement with exact solutions. To illustrate this method, we consider the linear harmonic oscillator and Coulomb potential confined within an impenetrable sphere of radius r C in three dimensions. © 2013 Wiley Periodicals, Inc.